This is a very original idea for a science project. I think you should be able to develop this idea into a really great project, but it will take some work and resources, and there is a limitation on what type of experiment you can do.

First, do an internet search on “physiological effects of ibuprofen, acetaminophen and rhinovirus,” to help you understand the mechanism of action of these anti-inflammatory agents and of the cold virus. For example, here is a paper reporting the physiological effects of ibuprofen on patients with sepsis. You are looking for scientific sources of information:

Unfortunately, it is not possible to do a science fair project with rhinoviruses because they are classified as biological safety level 3. You can do a project with a nonpathogenic virus that is classified as a BSL-1 or BSL-2, but not BSL-3: